Defined side streams

If AW AW the process of finding a linear-mixture basis can be tedious. Fortunately, however, in practical applications Nm is usually not greater than 2 or 3, and thus it is rarely necessary to search for more than one or two combinations of linearly independent columns for each reference vector. In the rare cases where A m > 3, the linear mixtures are often easy to identify. For example, in a tubular reactor with multiple side-injection streams, the side streams might all have the same inlet concentrations so that c(2) = = c(iVin). The stationary flow calculation would then require only AW = 1 mixture-fraction components to describe mixing between inlet 1 and the Nm — I side streams. In summary, as illustrated in Fig. 5.7, a turbulent reacting flow for which a linear-mixture basis exists can be completely described in terms of a transformed composition vector ipm( defined by... 

A similar volume defined injection protocol where the sample is confined within two controlled side streams of buffer solution has been developed by the group of Ramsey and has been dubbed pinched injection scheme [31]. The... 

For a completely homogeneous mixture, sc = 0 and thus v=0. Usually, two partial flows are combined in a mixing process. The volumetric flow ratio of the side stream with respect to the main stream is defined as ... 

Many times reactors are connected in series so that the exit stream of one reactor is the feed stream for another reactor. When this anangement is used it is often possible to speed calculations by defining conversion in terms of location at a point downstream rather than with respect to any single reactor. That is, the conversion X is the total number of moles of A that have reacted up to that point per mole of A fed to the first reactor. However, this definition can only be used provided that there are no side streams withdrawn and the feed stream enters o y the first reactor in the series. 

The envelop defined at this level of aggregation is delimited by the overall superstructure (see figure 6.1). The streams of mass and heat are given by ( ) the feed streams entering the structure (n) the product and side streams leaving the structure and Hi) all heat transferred to the structure. 

The energy for mixing comes mainly from the higher flow velocity in the side tee. Becanse there is a higher flow velocity, there must be a higher pressure to drive the side stream. This pressure loss is typically defined in terms of velocity head loss and depends on the design of the nozzle, which sets the head loss coefficient. 

Packie s (2) classic paper was the first to disclose criteria for defining fractionation between atmospheric tower distillate streams. Figure 2.6 is Packie s curve for fractionation between the overhead fraction and the adjacent side-stream. 

This subject has been discussed in detail earlier in this work. The only new point to be considered here is the definition of reflux from the draw tray. For purposes of Packie s analysis, reflux is defined as the volume of liquid falling from the tray below the draw tray. In terms of the first side stream draw tray, this is calculated by making a heat balance above Tray (Dl — 2) and then calculating the internal reflux from Tray (Dl - 1) which is required to absorb the excess heat. 

In the side-stream configuration, the MLSS is pumped through the membrane module. Side-stream systems typically use tubular membranes. Fouling is controlled by a well-defined flow velocity in the range of l-4m/s, generating a turbulent crossflow. Figure 9.7 shows a schematic view of a side-stream system. 

Alternatively, noting that the right-hand side of equations 11.77, 11.78 and 11.79 are independent of conditions below the feed plate, a stream N may be defined with mass equal to the difference between the vapour and liquid streams between two plates, of composition xd and of enthalpy Hd. The three quantities Vn, Ln+1, and N are then on a straight line passing through N, as shown in Figure 11.27. 

On the contrary, no general expression is available for calculating the mass-transfer coefficient at the shell side. In the literature, in fact, different equations are proposed, depending on the type of module and on the type of flow (parallel or crossflow). Probably, this is due to the fact that the fluidodynamics of the stream sent outside the fibers is strongly affected by the phenomena of channeling or bypassing and it is not well defined as for the stream, which is sent into the fibers. Hereinafter some of the different expressions proposed are reported. 

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